Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1606 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 1606 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10617506 | C2 | semidirect |
| 3. #10604981 | C2 | semidirect |
| 4. #10604220 | C2 | semidirect |
| 5. #10604168 | C2 | semidirect |
| 9. C2×C5×#124 | C4 | semidirect |
| 10. C2×#4093 | C4 | semidirect |
| 11. C2×#4086 | C4 | semidirect |
| 13. C2×#4030 | C4 | semidirect |
| 15. C2×#4020 | C4 | semidirect |
| 25. C22×C5×Q8 | C2×C4 | semidirect |
| 28. C22×C22⋊D5 | C2×C4 | semidirect |
| 34. C22×D20 | C2×C4 | semidirect |
| 35. C22×D20 | C2×C4 | semidirect |
| 37. C22×C4×D5 | C2×C4 | semidirect |
| 44. C2×C5×C22⋊C4 | C2×C4 | semidirect |
| 45. C2×C42×C5 | C2×C4 | semidirect |
| 48. C2×#685 | C2×C4 | semidirect |
| 50. C2×#683 | C2×C4 | semidirect |
| 51. C2×C4×Dic5 | C2×C4 | semidirect |
| 118. C2×#124 | AGL(1,𝔽5) | semidirect |
| 173. C22×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 201. C2×C22⋊C4 | C2×AGL(1,𝔽5) | semidirect |
| 203. C2×C42 | C2×AGL(1,𝔽5) | semidirect |
| 327. C5 | #21750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66008 | 2 |
| #10617506 | 2 |
| #10604981 | 2 |
| #10604220 | 2 |
| #10604168 | 2 |
| #21750 | 5 |